
from math import factorial





class 				UpperCAmelCase :




	'''simple docstring'''





	def __init__(			self   :					List[str]				,A   :					Optional[int]				,A   :					int					):
					__A       =					real
					if isinstance(A				,A					):
									__A       =					[1] * rank
					else:
									__A       =					rank






	def __repr__(			self   :					Tuple					):
					return (
					    f'''{self.real}+'''
					    f'''{'+'.join(str(A					)+'E'+str(n+1					)for n,dual in enumerate(self.duals					)					)}'''
					)






	def 							UpperCamelCase_    (			self   :					List[Any]					):
					__A       =					self.duals.copy()
					while cur[-1] == 0:
									cur.pop(-1					)
					return Dual(self.real				,A					)






	def __add__(			self   :					Optional[Any]				,A   :					List[Any]					):
					if not isinstance(A				,A					):
									return Dual(self.real + other				,self.duals					)
					__A       =					self.duals.copy()
					__A       =					other.duals.copy()
					if len(A					) > len(A					):
									o_dual.extend([1] * (len(A					) - len(A					))					)
					elif len(A					) < len(A					):
									s_dual.extend([1] * (len(A					) - len(A					))					)
					__A       =					[]
					for i in range(len(A					)					):
									new_duals.append(s_dual[i] + o_dual[i]					)
					return Dual(self.real + other.real				,A					)

	snake_case_          =	__add__






	def __sub__(			self   :					int				,A   :					Dict					):
					return self + other * -1






	def __mul__(			self   :					List[Any]				,A   :					List[str]					):
					if not isinstance(A				,A					):
									__A       =					[]
									for i in self.duals:
													new_duals.append(i * other					)
									return Dual(self.real * other				,A					)
					__A       =					[0] * (len(self.duals					) + len(other.duals					) + 1)
					for i, item in enumerate(self.duals					):
									for j, jtem in enumerate(other.duals					):
													new_duals[i + j + 1] += item * jtem
					for k in range(len(self.duals					)					):
									new_duals[k] += self.duals[k] * other.real
					for index in range(len(other.duals					)					):
									new_duals[index] += other.duals[index] * self.real
					return Dual(self.real * other.real				,A					)

	snake_case_          =	__mul__






	def __truediv__(			self   :					Tuple				,A   :					Dict					):
					if not isinstance(A				,A					):
									__A       =					[]
									for i in self.duals:
													new_duals.append(i / other					)
									return Dual(self.real / other				,A					)
					raise ValueError






	def __floordiv__(			self   :					List[str]				,A   :					Tuple					):
					if not isinstance(A				,A					):
									__A       =					[]
									for i in self.duals:
													new_duals.append(i // other					)
									return Dual(self.real // other				,A					)
					raise ValueError







	def __pow__(			self   :					Optional[Any]				,A   :					List[str]					):
					if n < 0 or isinstance(A				,A					):
									raise ValueError("power must be a positive integer"					)
					if n == 0:
									return 1
					if n == 1:
									return self
					__A       =					self
					for _ in range(n - 1					):
									x *= self
					return x





def 		UpperCAmelCase     (      a_						,  a_						,  a_		)						->      List[str]:







				"""simple docstring"""



				if not callable(a_		):
								raise ValueError("differentiate() requires a function as input for func"		)
				if not isinstance(a_						,  (float, int)		):
								raise ValueError("differentiate() requires a float as input for position"		)
				if not isinstance(a_						,  a_		):
								raise ValueError("differentiate() requires an int as input for order"		)
				__A       =					Dual(a_						,  1		)
				__A       =					func(a_		)
				if order == 0:
								return result.real
				return result.duals[order - 1] * factorial(a_		)


if __name__ == "__main__":
					import doctest

					doctest.testmod()


					def 		UpperCAmelCase     (      a_		)						->      Dict:







									"""simple docstring"""



									return y**2 * y**4
					print(differentiate(f, 9, 2))





from typing import Dict, List, Optional, Union

import numpy as np

from ...image_processing_utils import BaseImageProcessor, BatchFeature, get_size_dict
from ...image_transforms import (
    center_crop,
    convert_to_rgb,
    get_resize_output_image_size,
    normalize,
    rescale,
    resize,
    to_channel_dimension_format,
)
from ...image_utils import (
    OPENAI_CLIP_MEAN,
    OPENAI_CLIP_STD,
    ChannelDimension,
    ImageInput,
    PILImageResampling,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, is_vision_available, logging


a      :  List[str]			     =			logging.get_logger(__name__)


if is_vision_available():
	import PIL







class 				_a				(   _lowerCAmelCase					):
			A      		=	['''pixel_values''']

			def __init__(self,   SCREAMING_SNAKE_CASE_ = True,   SCREAMING_SNAKE_CASE_ = None,   SCREAMING_SNAKE_CASE_ = PILImageResampling.BICUBIC,   SCREAMING_SNAKE_CASE_ = True,   SCREAMING_SNAKE_CASE_ = None,   SCREAMING_SNAKE_CASE_ = True,   SCREAMING_SNAKE_CASE_ = 1 / 255,   SCREAMING_SNAKE_CASE_ = True,   SCREAMING_SNAKE_CASE_ = None,   SCREAMING_SNAKE_CASE_ = None,   SCREAMING_SNAKE_CASE_ = True,   **SCREAMING_SNAKE_CASE_,   )       ->   None:
						super().__init__(**SCREAMING_SNAKE_CASE_					)
						UpperCAmelCase_:		Optional[Any]							      =     size if size is not None else {"""shortest_edge""": 224}
						UpperCAmelCase_:		int							      =     get_size_dict(SCREAMING_SNAKE_CASE_,   default_to_square=SCREAMING_SNAKE_CASE_					)
						UpperCAmelCase_:		Dict							      =     crop_size if crop_size is not None else {"""height""": 224, """width""": 224}
						UpperCAmelCase_:		Union[str, Any]							      =     get_size_dict(SCREAMING_SNAKE_CASE_,   default_to_square=SCREAMING_SNAKE_CASE_,   param_name="""crop_size"""					)

						UpperCAmelCase_:		Optional[int]							      =     do_resize
						UpperCAmelCase_:		Optional[int]							      =     size
						UpperCAmelCase_:		Optional[int]							      =     resample
						UpperCAmelCase_:		Tuple							      =     do_center_crop
						UpperCAmelCase_:		Optional[int]							      =     crop_size
						UpperCAmelCase_:		str							      =     do_rescale
						UpperCAmelCase_:		Optional[int]							      =     rescale_factor
						UpperCAmelCase_:		List[str]							      =     do_normalize
						UpperCAmelCase_:		Any							      =     image_mean if image_mean is not None else OPENAI_CLIP_MEAN
						UpperCAmelCase_:		Dict							      =     image_std if image_std is not None else OPENAI_CLIP_STD
						UpperCAmelCase_:		Any							      =     do_convert_rgb

			def      __snake_case       (self,   SCREAMING_SNAKE_CASE_,   SCREAMING_SNAKE_CASE_,   SCREAMING_SNAKE_CASE_ = PILImageResampling.BICUBIC,   SCREAMING_SNAKE_CASE_ = None,   **SCREAMING_SNAKE_CASE_,   )       ->   np.ndarray:
						UpperCAmelCase_:		Optional[Any]							      =     get_size_dict(SCREAMING_SNAKE_CASE_,   default_to_square=SCREAMING_SNAKE_CASE_					)
						if "shortest_edge" not in size:
									raise ValueError(f'The `size` parameter must contain the key `shortest_edge`. Got {size.keys()}'					)
						UpperCAmelCase_:		Optional[Any]							      =     get_resize_output_image_size(SCREAMING_SNAKE_CASE_,   size=size["""shortest_edge"""],   default_to_square=SCREAMING_SNAKE_CASE_					)
						return resize(SCREAMING_SNAKE_CASE_,   size=SCREAMING_SNAKE_CASE_,   resample=SCREAMING_SNAKE_CASE_,   data_format=SCREAMING_SNAKE_CASE_,   **SCREAMING_SNAKE_CASE_					)

			def      __snake_case       (self,   SCREAMING_SNAKE_CASE_,   SCREAMING_SNAKE_CASE_,   SCREAMING_SNAKE_CASE_ = None,   **SCREAMING_SNAKE_CASE_,   )       ->   np.ndarray:
						UpperCAmelCase_:		Any							      =     get_size_dict(SCREAMING_SNAKE_CASE_					)
						if "height" not in size or "width" not in size:
									raise ValueError(f'The `size` parameter must contain the keys (height, width). Got {size.keys()}'					)
						return center_crop(SCREAMING_SNAKE_CASE_,   size=(size["""height"""], size["""width"""]),   data_format=SCREAMING_SNAKE_CASE_,   **SCREAMING_SNAKE_CASE_					)

			def      __snake_case       (self,   SCREAMING_SNAKE_CASE_,   SCREAMING_SNAKE_CASE_,   SCREAMING_SNAKE_CASE_ = None,   **SCREAMING_SNAKE_CASE_,   )       ->   Union[str, Any]:
						return rescale(SCREAMING_SNAKE_CASE_,   scale=SCREAMING_SNAKE_CASE_,   data_format=SCREAMING_SNAKE_CASE_,   **SCREAMING_SNAKE_CASE_					)

			def      __snake_case       (self,   SCREAMING_SNAKE_CASE_,   SCREAMING_SNAKE_CASE_,   SCREAMING_SNAKE_CASE_,   SCREAMING_SNAKE_CASE_ = None,   **SCREAMING_SNAKE_CASE_,   )       ->   np.ndarray:
						return normalize(SCREAMING_SNAKE_CASE_,   mean=SCREAMING_SNAKE_CASE_,   std=SCREAMING_SNAKE_CASE_,   data_format=SCREAMING_SNAKE_CASE_,   **SCREAMING_SNAKE_CASE_					)

			def      __snake_case       (self,   SCREAMING_SNAKE_CASE_,   SCREAMING_SNAKE_CASE_ = None,   SCREAMING_SNAKE_CASE_ = None,   SCREAMING_SNAKE_CASE_ = None,   SCREAMING_SNAKE_CASE_ = None,   SCREAMING_SNAKE_CASE_ = None,   SCREAMING_SNAKE_CASE_ = None,   SCREAMING_SNAKE_CASE_ = None,   SCREAMING_SNAKE_CASE_ = None,   SCREAMING_SNAKE_CASE_ = None,   SCREAMING_SNAKE_CASE_ = None,   SCREAMING_SNAKE_CASE_ = None,   SCREAMING_SNAKE_CASE_ = None,   SCREAMING_SNAKE_CASE_ = ChannelDimension.FIRST,   **SCREAMING_SNAKE_CASE_,   )       ->   PIL.Image.Image:
						UpperCAmelCase_:		Tuple							      =     do_resize if do_resize is not None else self.do_resize
						UpperCAmelCase_:		Tuple							      =     size if size is not None else self.size
						UpperCAmelCase_:		str							      =     get_size_dict(SCREAMING_SNAKE_CASE_,   param_name="""size""",   default_to_square=SCREAMING_SNAKE_CASE_					)
						UpperCAmelCase_:		List[str]							      =     resample if resample is not None else self.resample
						UpperCAmelCase_:		Optional[int]							      =     do_center_crop if do_center_crop is not None else self.do_center_crop
						UpperCAmelCase_:		Tuple							      =     crop_size if crop_size is not None else self.crop_size
						UpperCAmelCase_:		int							      =     get_size_dict(SCREAMING_SNAKE_CASE_,   param_name="""crop_size""",   default_to_square=SCREAMING_SNAKE_CASE_					)
						UpperCAmelCase_:		Union[str, Any]							      =     do_rescale if do_rescale is not None else self.do_rescale
						UpperCAmelCase_:		int							      =     rescale_factor if rescale_factor is not None else self.rescale_factor
						UpperCAmelCase_:		Tuple							      =     do_normalize if do_normalize is not None else self.do_normalize
						UpperCAmelCase_:		Dict							      =     image_mean if image_mean is not None else self.image_mean
						UpperCAmelCase_:		int							      =     image_std if image_std is not None else self.image_std
						UpperCAmelCase_:		Union[str, Any]							      =     do_convert_rgb if do_convert_rgb is not None else self.do_convert_rgb

						UpperCAmelCase_:		List[str]							      =     make_list_of_images(SCREAMING_SNAKE_CASE_					)

						if not valid_images(SCREAMING_SNAKE_CASE_					):
									raise ValueError(
									    """Invalid image type. Must be of type PIL.Image.Image, numpy.ndarray, """
									    """torch.Tensor, tf.Tensor or jax.ndarray."""					)

						if do_resize and size is None:
									raise ValueError("""Size must be specified if do_resize is True."""					)

						if do_center_crop and crop_size is None:
									raise ValueError("""Crop size must be specified if do_center_crop is True."""					)

						if do_rescale and rescale_factor is None:
									raise ValueError("""Rescale factor must be specified if do_rescale is True."""					)

						if do_normalize and (image_mean is None or image_std is None):
									raise ValueError("""Image mean and std must be specified if do_normalize is True."""					)

						# PIL RGBA images are converted to RGB
						if do_convert_rgb:
									UpperCAmelCase_:		Any							      =     [convert_to_rgb(SCREAMING_SNAKE_CASE_					) for image in images]

						# All transformations expect numpy arrays.
						UpperCAmelCase_:		List[str]							      =     [to_numpy_array(SCREAMING_SNAKE_CASE_					) for image in images]

						if do_resize:
									UpperCAmelCase_:		str							      =     [self.resize(image=SCREAMING_SNAKE_CASE_,   size=SCREAMING_SNAKE_CASE_,   resample=SCREAMING_SNAKE_CASE_					) for image in images]

						if do_center_crop:
									UpperCAmelCase_:		Dict							      =     [self.center_crop(image=SCREAMING_SNAKE_CASE_,   size=SCREAMING_SNAKE_CASE_					) for image in images]

						if do_rescale:
									UpperCAmelCase_:		Optional[Any]							      =     [self.rescale(image=SCREAMING_SNAKE_CASE_,   scale=SCREAMING_SNAKE_CASE_					) for image in images]

						if do_normalize:
									UpperCAmelCase_:		Dict							      =     [self.normalize(image=SCREAMING_SNAKE_CASE_,   mean=SCREAMING_SNAKE_CASE_,   std=SCREAMING_SNAKE_CASE_					) for image in images]

						UpperCAmelCase_:		Tuple							      =     [to_channel_dimension_format(SCREAMING_SNAKE_CASE_,   SCREAMING_SNAKE_CASE_					) for image in images]

						UpperCAmelCase_:		Union[str, Any]							      =     {"""pixel_values""": images}
						return BatchFeature(data=SCREAMING_SNAKE_CASE_,   tensor_type=SCREAMING_SNAKE_CASE_					)






